The function f ( x ) = 0.4 x 2 − 36 x + 1000 models the number of accidents, f(x), per 50 million miles driven as a function of a drivers age, x, in years, where x includes drivers from ages 16 through 74, inclusive. The graph of f is shown. Use the equation for f to solve Exercises 79-82. For what value of x does the graph reach its lowest point? Use the equation for f to find the minimum value of y. Describe the practical significance of this minimum value.
The function f ( x ) = 0.4 x 2 − 36 x + 1000 models the number of accidents, f(x), per 50 million miles driven as a function of a drivers age, x, in years, where x includes drivers from ages 16 through 74, inclusive. The graph of f is shown. Use the equation for f to solve Exercises 79-82. For what value of x does the graph reach its lowest point? Use the equation for f to find the minimum value of y. Describe the practical significance of this minimum value.
Solution Summary: The author explains how to calculate the value of x at the lowest point on the graph and the minimum value for y using the equation f(x)=0.4x 2-36
The function
f
(
x
)
=
0.4
x
2
−
36
x
+
1000
models the number of accidents, f(x), per 50 million miles driven as a function of a drivers age, x, in years, where x includes drivers from ages 16 through 74, inclusive. The graph of f is shown. Use the equation for f to solve Exercises 79-82.
For what value of x does the graph reach its lowest point? Use the equation for f to find the minimum value of y. Describe the practical significance of this minimum value.
Under a microscope, Ms. Kapinski studies a culture with bacteria. As the number of hours progresses, Ms. Kapinski sees that the bacteria can be modeled by the function ?(?) = 1290(0.76) ? where b represents the number of bacteria t hours after Ms. Kapinski begins her study.
(a) What does the value 0.76 represent in this situation? Be sure to explain.
(b) What does the value 1290 represent in this situation? Be sure to explain.
(c) The number of bacteria in a second study is modeled by the function ?2 (?) = 1180(1.76) ? .
i. What does the value of 1180 represent in this situation?
ii. What does the difference of 1290 and 1180 mean between the two studies?
iii. What does the difference between 0.76 and 1.76 mean between the two studies?
Use a graphing utility to construct a table of values for the function f(x) = 7−x.Then sketch the graph of the function.
The equation for f is given by the simplified expression that results after performing the indicated operation (x - 1/x) / (x + 1/x). Write the equation for f and then graph the function.
Chapter 7 Solutions
Thinking Mathematically, Books a la Carte Edition plus MyLab Math with Pearson eText -- Access Card Package, 4/e (7th Edition)
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Area Between The Curve Problem No 1 - Applications Of Definite Integration - Diploma Maths II; Author: Ekeeda;https://www.youtube.com/watch?v=q3ZU0GnGaxA;License: Standard YouTube License, CC-BY